Pre-Algebra Examples

Graph 6y=10x-32
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 1.3
Simplify the right side.
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Step 1.3.1
Simplify each term.
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Step 1.3.1.1
Cancel the common factor of and .
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Step 1.3.1.1.1
Factor out of .
Step 1.3.1.1.2
Cancel the common factors.
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Step 1.3.1.1.2.1
Factor out of .
Step 1.3.1.1.2.2
Cancel the common factor.
Step 1.3.1.1.2.3
Rewrite the expression.
Step 1.3.1.2
Cancel the common factor of and .
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Step 1.3.1.2.1
Factor out of .
Step 1.3.1.2.2
Cancel the common factors.
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Step 1.3.1.2.2.1
Factor out of .
Step 1.3.1.2.2.2
Cancel the common factor.
Step 1.3.1.2.2.3
Rewrite the expression.
Step 1.3.1.3
Move the negative in front of the fraction.
Step 2
Rewrite in slope-intercept form.
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Step 2.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 2.2
Reorder terms.
Step 3
Use the slope-intercept form to find the slope and y-intercept.
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Step 3.1
Find the values of and using the form .
Step 3.2
The slope of the line is the value of , and the y-intercept is the value of .
Slope:
y-intercept:
Slope:
y-intercept:
Step 4
Any line can be graphed using two points. Select two values, and plug them into the equation to find the corresponding values.
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Step 4.1
Reorder terms.
Step 4.2
Find the x-intercept.
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Step 4.2.1
To find the x-intercept(s), substitute in for and solve for .
Step 4.2.2
Solve the equation.
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Step 4.2.2.1
Rewrite the equation as .
Step 4.2.2.2
Combine and .
Step 4.2.2.3
Add to both sides of the equation.
Step 4.2.2.4
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Step 4.2.2.5
Divide each term in by and simplify.
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Step 4.2.2.5.1
Divide each term in by .
Step 4.2.2.5.2
Simplify the left side.
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Step 4.2.2.5.2.1
Cancel the common factor of .
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Step 4.2.2.5.2.1.1
Cancel the common factor.
Step 4.2.2.5.2.1.2
Divide by .
Step 4.2.3
x-intercept(s) in point form.
x-intercept(s):
x-intercept(s):
Step 4.3
Find the y-intercept.
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Step 4.3.1
To find the y-intercept(s), substitute in for and solve for .
Step 4.3.2
Solve the equation.
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Step 4.3.2.1
Multiply by .
Step 4.3.2.2
Remove parentheses.
Step 4.3.2.3
Simplify .
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Step 4.3.2.3.1
Multiply by .
Step 4.3.2.3.2
Subtract from .
Step 4.3.3
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
Step 4.4
Create a table of the and values.
Step 5
Graph the line using the slope and the y-intercept, or the points.
Slope:
y-intercept:
Step 6